For future reference:

$ mix phx.new react_demo --no-ecto

* creating react_demo/config/config.exs
...
* creating react_demo/assets/static/robots.txt

Fetch and install dependencies? [Yn] Y
* running mix deps.get
* running cd assets && npm install && node node_modules/webpack/bin/webpack.js --mode development
* running mix deps.compile

We are almost there! The following steps are missing:

    $ cd react_demo

Start your Phoenix app with:

    $ mix phx.server

You can also run your app inside IEx (Interactive Elixir) as:

    $ iex -S mix phx.server

$ cd react_demo

react_demo$ mix phx.server
Compiling 12 files (.ex)
Generated react_demo app
[info] Running ReactDemoWeb.Endpoint with cowboy 2.6.3 at 0.0.0.0:4000 (http)
[info] Access ReactDemoWeb.Endpoint at http://localhost:4000

Webpack is watching the files…

Hash: 1fc94cc9b786e491ad40
Version: webpack 4.4.0
Time: 513ms
Built at: 7/12/2019 1:08:54 PM
                Asset       Size       Chunks             Chunk Names
       ../css/app.css   10.6 KiB  ./js/app.js  [emitted]  ./js/app.js
               app.js   7.26 KiB  ./js/app.js  [emitted]  ./js/app.js
       ../favicon.ico   1.23 KiB               [emitted]  
../images/phoenix.png   13.6 KiB               [emitted]  
        ../robots.txt  202 bytes               [emitted]  
   [0] multi ./js/app.js 28 bytes {./js/app.js} [built]
[../deps/phoenix_html/priv/static/phoenix_html.js] 2.21 KiB {./js/app.js} [built]
[./css/app.css] 39 bytes {./js/app.js} [built]
[./js/app.js] 493 bytes {./js/app.js} [built]
    + 2 hidden modules
Child mini-css-extract-plugin node_modules/css-loader/dist/cjs.js!css/app.css:
    [./node_modules/css-loader/dist/cjs.js!./css/app.css] 284 bytes {mini-css-extract-plugin} [built]
    [./node_modules/css-loader/dist/cjs.js!./css/phoenix.css] 10.9 KiB {mini-css-extract-plugin} [built]
        + 1 hidden module

Check in the browser http://localhost:4000/ to see the “Phoenix Framework” page.

^C
BREAK: (a)bort (c)ontinue (p)roc info (i)nfo (l)oaded
       (v)ersion (k)ill (D)b-tables (d)istribution
a

react_demo $ cd assets

assets $ npm i -g npm-check-updates
.npm-global/bin/npm-check-updates -> .npm-global/lib/node_modules/npm-check-updates/bin/npm-check-updates
.npm-global/bin/ncu -> .npm-global/lib/node_modules/npm-check-updates/bin/ncu
+ npm-check-updates@3.1.18
added 260 packages from 118 contributors in 8.122s

assets $ ncu -u

Upgrading react_demo/assets/package.json
[====================] 12/12 100%

 @babel/core                          ^7.0.0  →  ^7.5.4 
 @babel/preset-env                    ^7.0.0  →  ^7.5.4 
 babel-loader                         ^8.0.0  →  ^8.0.6 
 copy-webpack-plugin                  ^4.5.0  →  ^5.0.3 
 css-loader                           ^2.1.1  →  ^3.0.0 
 mini-css-extract-plugin              ^0.4.0  →  ^0.7.0 
 optimize-css-assets-webpack-plugin   ^4.0.0  →  ^5.0.3 
 uglifyjs-webpack-plugin              ^1.2.4  →  ^2.1.3 
 webpack                               4.4.0  →  4.35.3 
 webpack-cli                         ^2.0.10  →  ^3.3.5 

Run npm install to install new versions.

assets $ npm i

npm WARN assets No description

added 119 packages from 103 contributors, removed 596 packages, updated 72 packages, moved 3 packages and audited 8034 packages in 17.606s
found 63 high severity vulnerabilities
  run `npm audit fix` to fix them, or `npm audit` for details

assets $ npm i -D  @babel/preset-react

npm WARN assets No description

+ @babel/preset-react@7.0.0
added 7 packages from 1 contributor and audited 8056 packages in 4.55s
found 63 high severity vulnerabilities
  run `npm audit fix` to fix them, or `npm audit` for details

assets $ npm i -P react react-dom

npm WARN assets No description

+ react@16.8.6
+ react-dom@16.8.6
added 5 packages and audited 8082 packages in 4.779s
found 63 high severity vulnerabilities
  run `npm audit fix` to fix them, or `npm audit` for details
assets $ 

Delete assets/.babelrc

assets $ rm .babelrc

Create assets/babel.config.js

module.exports = function (api) {
  api.cache(true);

  const presets = [
    '@babel/preset-env',
    '@babel/preset-react',
  ]
  const plugins = [
  ]

  return {
    presets,
    plugins
  };
}

Modify assets/webpack.config.js

const path = require('path');
const glob = require('glob');
const MiniCssExtractPlugin = require('mini-css-extract-plugin');
const UglifyJsPlugin = require('uglifyjs-webpack-plugin');
const OptimizeCSSAssetsPlugin = require('optimize-css-assets-webpack-plugin');
const CopyWebpackPlugin = require('copy-webpack-plugin');

module.exports = (env, options) => ({
  optimization: {
    minimizer: [
      new UglifyJsPlugin({ cache: true, parallel: true, sourceMap: false }),
      new OptimizeCSSAssetsPlugin({})
    ]
  },
  entry: {
    './js/app.js': glob.sync('./vendor/**/*.js').concat(['./js/app.js'])
  },
  output: {
    filename: 'app.js',
    path: path.resolve(__dirname, '../priv/static/js')
  },
  module: {
    rules: [
      {
        test: /\.(js|jsx)$/, /* add jsx */
        exclude: /node_modules/,
        use: {
          loader: 'babel-loader'
        }
      },
      {
        test: /\.css$/,
        use: [MiniCssExtractPlugin.loader, 'css-loader']
      }
    ]
  },
  plugins: [
    new MiniCssExtractPlugin({ filename: '../css/app.css' }),
    new CopyWebpackPlugin([{ from: 'static/', to: '../' }])
  ]
});

Modify assets/js/app.js:

// We need to import the CSS so that webpack will load it.
// The MiniCssExtractPlugin is used to separate it out into
// its own CSS file.
import css from "../css/app.css"

// webpack automatically bundles all modules in your
// entry points. Those entry points can be configured
// in "webpack.config.js".
//
// Import dependencies
//
import "phoenix_html"

// Import local files
//
// Local files can be imported directly using relative paths, for example:
// import socket from "./socket"

import React from 'react'
import ReactDOM from 'react-dom'

const App = ({ title }) =>
  <div>{title}</div>

const title = "Hello World!"

ReactDOM.render(
    <App title={title} />,
  document.getElementById('app')
)

Replace contents of react_demo/lib/react_demo_web/templates/page/index.html.eex with

<div id="app"></div>

$ cd ..

react_demo $ mix phx.server

Compiling 1 file (.ex)
[info] Running ReactDemoWeb.Endpoint with cowboy 2.6.3 at 0.0.0.0:4000 (http)
[info] Access ReactDemoWeb.Endpoint at http://localhost:4000

webpack is watching the files…

Hash: 422aabb9c911039eccdd
Version: webpack 4.35.3
Time: 683ms
Built at: 07/12/2019 2:00:54 PM
                Asset       Size       Chunks             Chunk Names
       ../css/app.css   10.6 KiB  ./js/app.js  [emitted]  ./js/app.js
       ../favicon.ico   1.23 KiB               [emitted]  
../images/phoenix.png   13.6 KiB               [emitted]  
        ../robots.txt  202 bytes               [emitted]  
               app.js    911 KiB  ./js/app.js  [emitted]  ./js/app.js
Entrypoint ./js/app.js = ../css/app.css app.js
[0] multi ./js/app.js 28 bytes {./js/app.js} [built]
[../deps/phoenix_html/priv/static/phoenix_html.js] 2.21 KiB {./js/app.js} [built]
[./css/app.css] 39 bytes {./js/app.js} [built]
[./js/app.js] 790 bytes {./js/app.js} [built]
[./node_modules/webpack/buildin/global.js] (webpack)/buildin/global.js 472 bytes {./js/app.js} [built]
    + 13 hidden modules
Child mini-css-extract-plugin node_modules/css-loader/dist/cjs.js!css/app.css:
    Entrypoint mini-css-extract-plugin = *
    [./node_modules/css-loader/dist/cjs.js!./css/app.css] 282 bytes {mini-css-extract-plugin} [built]
    [./node_modules/css-loader/dist/cjs.js!./css/phoenix.css] 10.9 KiB {mini-css-extract-plugin} [built]
        + 1 hidden module

Looking at http://localhost:4000/ you should see:

react_demo2178×472 56.9 KB

The resulting assets/package.json:

{
  "repository": {},
  "license": "MIT",
  "scripts": {
    "deploy": "webpack --mode production",
    "watch": "webpack --mode development --watch"
  },
  "dependencies": {
    "phoenix": "file:../deps/phoenix",
    "phoenix_html": "file:../deps/phoenix_html",
    "react": "^16.8.6",
    "react-dom": "^16.8.6"
  },
  "devDependencies": {
    "@babel/core": "^7.5.4",
    "@babel/preset-env": "^7.5.4",
    "@babel/preset-react": "^7.0.0",
    "babel-loader": "^8.0.6",
    "copy-webpack-plugin": "^5.0.3",
    "css-loader": "^3.0.0",
    "mini-css-extract-plugin": "^0.7.0",
    "optimize-css-assets-webpack-plugin": "^5.0.3",
    "uglifyjs-webpack-plugin": "^2.1.3",
    "webpack": "4.35.3",
    "webpack-cli": "^3.3.5"
  }
}

Glad we managed to help

If I understand it correctly:

• webpack is using assets/ as the root directory
• therefore assets/babel.config.js is in the root directory
• the default is rootMode: "root"
• so it “just works”

"upward" is necessary when your configuration file in a parent directory is controlling the configuration of multiple Node.js projects below it.

const HelloReact = () => {
  return <div>Hello World</div>;
}

Is that your file?

I think You miss this…

import React from 'react';

Even if it is not visible, You need to import React before using this code

<div>...</div>

because it uses React.createElement() under the hood

Also this tutorial should offer you a complete introduction to react and babel config the right way.